Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
Correct Answer
$6858
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5400 × 3% × 9
= $5400 ×3/100 × 9
= 5400 × 3 × 9/100
= 16200 × 9/100
= 145800/100
= $1458
Thus, Simple Interest = $1458
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 9)
= $5400 + ($5400 ×3/100 × 9)
= $5400 + (5400 × 3 × 9/100)
= $5400 + (16200 × 9/100)
= $5400 + (145800/100)
= $5400 + $1458 = $6858
Thus, Amount (A) to be paid = $6858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $162 × 9 = $1458
Thus, Simple Interest (SI) = $1458
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(7) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.